few_shots: Example:
Problem/activity:
Task
 Arrange the fractions in order from least to greatest. Explain your answer with a picture.
 $\frac{1}{5}, \frac{1}{7}, \frac{1}{3} $
 $\frac{2}{5}, \frac{2}{7}, \frac{2}{3} $
 $\frac{5}{6}, \frac{3}{6}, \frac{1}{6} $
 $\frac{5}{12}, \frac{8}{12}, \frac{4}{12} $

Standard options: 
A. Understand a fraction as a number on the number line; represent fractions on a number line diagram.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
B. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
C. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.


Thought: By arranging the fractions in this problem, students learn to compare fractions by reasoning about their size.
Answer: B

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: im_task_000157

3
options: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
problem_activity: Optional activity
The mathematical purpose of this activity is for students to collect, summarize, interpret, and draw conclusions from bivariate data using scatter plots, best fit lines, residuals and correlation coefficients. Students measure the approximate lengths of the humerus bone and height of their classmates to collect data and create a linear model. The model is then used to approximate the height of an ancient human based on the length of a found humerus bone.
Making graphing technology available gives students an opportunity to choose appropriate tools strategically (MP5). By collecting their own data and using a best fit line to find additional information, students are modeling with mathematics (MP4).
Launch
Arrange students in groups of 2 to 4. Present the task to students and ask students to brainstorm different ways that they could answer the question. After 2 minutes of quiet think time, ask students to share their ideas with the class. The remaining time should be used by students to collect, analyze, summarize, and interpret the data.
Speaking, Reading: MLR5 Co-Craft Questions.
Use this routine to help students further interpret and increase awareness of the language used to talk about scatter plots, best fit lines, residuals and correlation coefficients. Display the first sentence of this problem (“An anthropologist finds a fossilized humerus bone of an ancient human ancestor.”), and ask students to write down possible mathematical questions that could be asked about the situation. Invite students to compare their questions before revealing the remainder of the question. Listen for and amplify any questions involving comparing bivariate data.
Design Principle(s): Maximize meta-awareness; Support sense-making
Student Facing
[IMG]
An anthropologist finds a fossilized humerus bone of an ancient human ancestor. The humerus is an arm bone running from the shoulder to the elbow. It is 24 centimeters in length. Use data from your classmates to estimate the height of this ancient human.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Anticipated Misconceptions
Students may find it difficult to start to answer the question. Ask students what are the variables given in the situation. Ask students if there is a way we could collect information from people in the classroom to help answer the question.
Activity Synthesis
The purpose of this discussion is for students to communicate how they used mathematics to justify their findings.
Ask students:
“How confident are you in your answer? What information helped you determine your confidence?” (Not very confident. Since the correlation coefficient is near 0.6, there is only a moderate relationship between height and humerus length. Additionally, this ancient human ancestor may have a different anatomy—for example, apes tend to have proportionally longer arms than humans do.)
“How did you use mathematics to estimate the height of the ancient human?” (First, I collected data on the height and the approximate length of the humerus of my classmates. I then made a scatter plot to determine whether or not a linear model was appropriate, and then computed a line of best fit. I substituted 24 centimeters into my line of best fit and obtained my answer.)
“Do you think that the way you measured the humerus of your classmates impacted your choice of linear model? Explain your reasoning.” (Yes, I think that I probably overestimated the bone length, because I was measuring from the outside and not the inside. I think that my model likely overestimates height.)


correct_option_index: 1